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4/5 of the elements in set D are equal to x, and the

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marcodonzelli
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4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 10:14
4/5 of the elements in set D are equal to x, and the remaining elements in D are equal to y. What is the value of Ix-yI if the standard deviation of D is 400?

500
600
800
1000
1200



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Re: 4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 11:45
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E

\(x_{av}=\frac45*x+\frac15*y\)

\(D=\sqrt{\frac45*(x-(\frac45*x+\frac15*y))^2+\frac15*(y-(\frac45*x+\frac15*y))^2}\)

\(D=\sqrt{\frac{4}{5^3}*(x-y)^2+\frac{4^2}{5^3}*(x-y)^2}\)

\(D=\sqrt{\frac{12}{5^3}}*|x-y|\)

\(|x-y|=400*\frac{5}{2}*\sqrt{\frac{5}{3}}=1000*\sqrt{1.(6)}\)

\(1200<|x-y|<1300\)
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Re: 4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 11:54
walker wrote:
E

\(x_{av}=\frac45*x+\frac15*y\)

\(D=\sqrt{\frac45*(x-(\frac45*x+\frac15*y))^2+\frac15*(y-(\frac45*x+\frac15*y))^2}\)

\(D=\sqrt{\frac{4}{5^3}*(x-y)^2+\frac{4^2}{5^3}*(x-y)^2}\)

\(D=\sqrt{\frac{12}{5^3}}*|x-y|\)

\(|x-y|=400*\frac{5}{2}*\sqrt{\frac{5}{3}}=1000*\sqrt{1.(6)}\)

\(1200<|x-y|<1300\)



no man, assume x=0....
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Re: 4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 11:58
marcodonzelli wrote:
walker wrote:
E

\(x_{av}=\frac45*x+\frac15*y\)

\(D=\sqrt{\frac45*(x-(\frac45*x+\frac15*y))^2+\frac15*(y-(\frac45*x+\frac15*y))^2}\)

\(D=\sqrt{\frac{4}{5^3}*(x-y)^2+\frac{4^2}{5^3}*(x-y)^2}\)

\(D=\sqrt{\frac{12}{5^3}}*|x-y|\)

\(|x-y|=400*\frac{5}{2}*\sqrt{\frac{5}{3}}=1000*\sqrt{1.(6)}\)

\(1200<|x-y|<1300\)



no man, assume x=0....


E can not be:

1200 is not in the interval 1200<X-Y<1500
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Re: 4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 12:50
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D

\(x_{av}=\frac45*x+\frac15*y\)

\(D=\sqrt{\frac45*(x-(\frac45*x+\frac15*y))^2+\frac15*(y-(\frac45*x+\frac15*y))^2}\)

\(D=\sqrt{\frac{4}{5^3}*(x-y)^2+\frac{4^2}{5^3}*(x-y)^2}\)

\(D=\sqrt{\frac{20}{5^3}}*|x-y|\)

\(|x-y|=400*\frac{5}{2}=1000\)
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Re: 4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 13:05
walker wrote:
D

\(x_{av}=\frac45*x+\frac15*y\)

\(D=\sqrt{\frac45*(x-(\frac45*x+\frac15*y))^2+\frac15*(y-(\frac45*x+\frac15*y))^2}\)

\(D=\sqrt{\frac{4}{5^3}*(x-y)^2+\frac{4^2}{5^3}*(x-y)^2}\)

\(D=\sqrt{\frac{20}{5^3}}*|x-y|\)

\(|x-y|=400*\frac{5}{2}=1000\)


yes, this is right. How long did it take to solve this problem?
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Re: 4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 13:13
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I knew the way just after I'd read the problem but spent more than 2min...
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Re: 4/5 of the elements in set D are equal to x, and the [#permalink] New post   25 Jan 2008, 13:19
D, it took me 1 min.

(x-m)^2*(4/5) + (y-m)^2*(1/5) = stdev^2, m = 4/5x+1/5y

4/5*1/5*(x-y)^2 = stdev^2 -> abs(x-y) = stdev*5/2 = 1000



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Re: 4/5 of the elements in set D are equal to x, and the [#permalink]
25 Jan 2008, 13:19
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